Contact information
Name:
c. jayne trent
Phone:
610-330-5267
Email:
trentj@lafayette.edu
Two matroids are commonly defined on a graph: the familiar cycle matroid and the
more rarely-encountered bicircular matroid.
The bases of the cycle matroid are the spanning trees of the associated graph;
the bases of the bicircular matroid are all subgraphs of the graph where each
connected component contains exactly one cycle and (possibly) other edges.
We enumerate the bases of the bicircular matroid for several classes of graphs.
For a given graph, usually there are more bases of the bicircular matroid than
the cycle matroid. We ask when the reverse is true, and what this translates
to in terms of the structure of the graph.
No prior knowledge of matroids or graphs is needed.